Exponential stability of laminated beams with structural damping and Coleman–Gurtin heat law

Abstract This work aims to investigate the exponential stability of a one-dimensional thermoelastic laminated beam with structural damping, considering the effect of the heat flux governed by the Coleman–Gurtin thermal law on the effective rotation angle equation. Using the energy method, we demonstrate the exponential stability if the wave speeds are equal. Furthermore, using Gearhart–Herbst–Prüss–Huang’s theorem, we demonstrate the lack of exponential stability if the wave speeds are different.